Question

If f(x) = (1+x+x2+x3+.......x2012)2−x2012(1+x+x2+x3+.......x2012)2−x2012
g(x) = 1+x+x2+x3+.......x20111+x+x2+x3+.......x2011 
Then what is the remainder when f(x) is divided by g(x)​

Answer 1

in simple way...  

put x=1

f(1)=(2012)^2-1

g(1)=2011

f(1)/g(1)=[(2012)^2-1]/[2011]

=[(2012+1)*(2012-1)]/[2011]

=[(2013)*(2011)]/[2011]

=2013

hence reminder is 0